
Recent Posts
Archives
 November 2016
 April 2015
 March 2015
 February 2015
 November 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 March 2013
 July 2012
 March 2012
 December 2011
Categories
 Adobe Reader AUCTeX autopair blogging bug C cllib closure Common Lisp comparison dash debug documentary dynamic scoping elisp ELPA English entropy ergodic theory export exposition fish fix font gotcha html htmlize image immutable information theory Internet intuition Japanese javascript JPEG js2mode KAIST keyboard kimchi Korea LaTeX lexicalbinding lexical scoping LuaTeX managed measure theory monospace movie mutable namespace NEF orgmode package PDF Photoshop PNG pointer portable prefix process Python rainbowdelimiters region rice SLIME specialvariable stew tablet Ubuntu unicode Windows Windows 8 wireless Wordpress XeTeX
Meta
Category Archives: Mathematics
Introduction to Wasserstein metric (earth mover’s distance)
Table of Contents 1. the cost of moving one particle 2. The cost of moving a finite collection of particles of total mass 1. 3. coupling 4. composing 5. definition of the Wasserstein distance 6. Moving a collection of particles … Continue reading
Intuitions on problems from Elements of Information Theory Chapter 2
Table of Contents 1. meaning of conditional mutual information 2. comments on some selected problems from Chapter 2 2.1. Problem 2.6 2.2. Problem 2.14 2.3. Problem 2.23 2.4. Problem 2.27 2.5. Problem 2.41 This post is not about sharing solutions … Continue reading
Posted in Mathematics
Tagged entropy, information theory, intuition, mutual information
Leave a comment
DoobDynkin Lemma for probability space
Table of Contents 1. Proof 1 2. Proof 2 3. Proof 3 4. Uniqueness of H 5. applications Let f, g be measurable functions from a probability space to measurable spaces and respectively. Consider the following three conditions: (1) (in … Continue reading
Proofs of DoobDynkin Lemma
Table of Contents 1. uniqueness of H 2. counterexamples 3. proof when g has a countable range, with nice Y 4. proof when Y is the Cantor space 5. proof when Y is the unit interval 6. proof for standard … Continue reading
Small introduction to Hausdorff distance
Table of Contents 1. motivation and intuition 2. coming up with the two definitions of the Hausdorff distance 3. more exercises Update: I realized that parts of this post focus on unimportant small details. Sorry for that, you may skip … Continue reading
mod 0 equivalence of subsigmaalgebras and gotchas
Table of Contents 1. closure of a subsigmaalgebra 2. closed sub sigma algebra 3. mod zero equivalence of sub sigma algebras When we are building some theory involving measures, there are cases where we should ignore null sets (sets of … Continue reading
using orgmode export feature to publish to wordpress with math equations
Table of Contents some preliminary search and replace some idea on how to write a math blog post using orgmode, AUCTeX, latexpreview If you are using the latest official version of Emacs and the latest version of orgmode, which is … Continue reading